Model-based control of constrained nonlinear process systems

Thomas Andrew Kendi, Purdue University

Abstract

A nonlinear anti-windup scheme for input-output linearization is developed. The synthesis scheme employs a state-dependent constraint operator, a mapping of the physical constraints onto the transformed input, within a linear model-based anti-windup approach. The resultant nonlinear anti-windup controller is shown to solve an instantaneous 1-norm minimization to guarantee closed-loop performance. Nominal closed-loop stability conditions are obtained using conic sector bounds and nonlinear $\mu$-analysis. The application of the "constraint-mapping" anti-windup approach for two reactor case studies resulted in a performance improvement over comparable linear control strategies. The partitioned nonlinear inverse serves as the foundation for a competing approach to nonlinear anti-windup synthesis. An extension to the nonlinear internal model control (NLIMC) framework which incorporates anti-windup and measured disturbance compensation is developed. For control affine systems with a characteristic matrix of a specific structure, the NLIMC-based anti-windup controller exactly solves an instantaneous 1-norm minimization. A controller which approximately solves the instantaneous minimization is obtained using a two-step design procedure. For a styrene polymerization case study, the NLIMC-based anti-windup controller significantly outperforms a linear controller for measured disturbance rejection and a hypothetical grade change. Extensions to nonminimum phase systems are documented in theory and in application through a CSTR case study. The development of controllers for constrained nonlinear systems with uncertainty and bounded unmeasured disturbances using quadratic Lyapunov theory is presented. Application of the Lyapunov-based synthesis scheme requires that the nonlinear system is converted into a linear system with state-dependent parameters. The state-dependent parameters are evaluated at the input and output bounds to obtain a polytope of linear plants which bounds the nonlinear system. A linear state-feedback controller is obtained for the polytope of linear plants which guarantees that the magnitude of the system output and the controlled input lie within specified bounds for a class of unmeasured disturbances. The boundaries of the polytope can be expanded to incorporate structured uncertainty from the nonlinear system. The controller gain is obtained by iteratively solving linear matrix inequalities.

Degree

Ph.D.

Advisors

Doyle, Purdue University.

Subject Area

Chemical engineering|Operations research

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